# Referee Response: Health Mediation Path Check

## Path a: Z → health_exp_gdp

N = 4110, Countries = 175, R² = 0.2701

| Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|
| Z_1 | -2.5870 | 1.9642 | 0.1879 |  |
| Z_2 | 0.5924 | 0.2875 | 0.0394 | ** |
| Z_3 | -0.0280 | 0.0117 | 0.0166 | ** |
| rgdp_growth | -0.0120 | 0.0010 | 0.0000 | *** |
| kaopen | 0.0057 | 0.0236 | 0.8082 |  |

## Path b: health_exp_gdp → patents_per_million

N = 854, Countries = 53, R² = -0.0103

| Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|
| health_exp_gdp | 5.9868 | 9.4828 | 0.5280 |  |
| rgdp_growth | 0.5586 | 0.6508 | 0.3910 |  |
| kaopen | 4.5112 | 9.9096 | 0.6491 |  |

## Path c: Z + health → patents_per_million

N = 854, Countries = 53, R² = 0.1269

| Variable | Coef | SE | p-value | Sig |
|---|---|---|---|---|
| Z_1 | -1058.2793 | 1207.5258 | 0.3811 |  |
| Z_2 | 171.1660 | 170.8825 | 0.3168 |  |
| Z_3 | -6.5685 | 6.7285 | 0.3292 |  |
| health_exp_gdp | 1.5459 | 9.5762 | 0.8718 |  |
| rgdp_growth | 0.3863 | 0.6532 | 0.5544 |  |
| kaopen | 2.4227 | 9.9344 | 0.8074 |  |

## Verdict
- Path a (Z_1 → health_exp): p = 0.1879 → **not significant**
- Path b (health → patents_pm): p = 0.5280 → **not significant**

**Both paths are insignificant.** The mediation claim (53.6%) should be dropped or heavily qualified.
